Fractional Derivatives, Memory Kernels and Solution of a Free Electron Laser Volterra Type Equation

Marcello Artioli, Giuseppe Dattoli, Silvia Licciardi and Simonetta Pagnutti
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Marcello Artioli: ENEA—Bologna Research Center, Via Martiri di Monte Sole, 4, 40129 Bologna, Italy
Giuseppe Dattoli: ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
Silvia Licciardi: ENEA—Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
Simonetta Pagnutti: ENEA—Bologna Research Center, Via Martiri di Monte Sole, 4, 40129 Bologna, Italy

Mathematics, 2017, vol. 5, issue 4, 1-9

Abstract: The high gain free electron laser (FEL) equation is a Volterra type integro-differential equation amenable for analytical solutions in a limited number of cases. In this note, a novel technique, based on an expansion employing a family of two variable Hermite polynomials, is shown to provide straightforward analytical solutions for cases hardly solvable with conventional means. The possibility of extending the method by the use of expansion using different polynomials (two variable Legendre like) expansion is also discussed.

Keywords: free electron laser (FEL); Volterra equations; iterative solutions; Hermite polynomials; Legendre polynomials (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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